[VA] SRC#004- Fun with Sexagesimal Trigs
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02-12-2019, 04:39 PM
(This post was last modified: 02-12-2019 04:41 PM by Albert Chan.)
Post: #11
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RE: [VA] SRC#004- Fun with Sexagesimal Trigs
Prove C = 1:
Using shorthand c(#) = c# = cos(#°), s(#) = s# = sin(#°) C = (1 - c61/c1)(1 - c62/c2) ... (1 - c119/c59) center = (1 + c90/c30) = (1 + 0/c30) = 1 Check the edges, each pair P had the form: = (1 - c(90-x)/c(30-x)) * (1 - c(90+x)/c(30+x)) = (1 - sx / c(30-x)) * (1 + sx / c(30+x)) To simplify P, we need these identities: cos(A+B) = cos(A)cos(B) − sin(A)sin(B) cos(A−B) = cos(A)cos(B) + sin(A)sin(B) Removing the annoying denominator, let k = c(30-x) * c(30+x) k P = (c(30+x) - sx) * (c(30-x) + sx) = k + sx^2 + sx * (c(30+x) - c(30-x)) = k + sx^2 + sx * (-2 s(30) sx) = k + sx^2 − sx^2 = k -> P = 1 All factors can considered value of 1, thus C = 1 |
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